Putting in priors by hand (DCE)

[Larmor]

Hi,

I'm doing a DCE study with 6 attributes, each with 3 levels, and it is clear that each of these attributes will have a positive coefficient in the utility function (i.e., every attribute is something favourable that respondents would want more of). I can put in small positive values like so

Code: Select all

;alts=package1*,package2*
;rows=12
;eff=(mnl,d)
;model:
U(package1)=b2[0.05]*att2[12,18,24] + b3[0.05]*att3[30,55,80]+ b4[0.05]*att4[1,2,3] + b5[0.05]*att5[1,2,3] + b6[0.05]*att6[50,75,100] + b7[0.05]*att7[1,2,3] /
U(package2)=b2*att2+ b3*att3+ b4*att4+ b5*att5+ b6*att6+ b7*att7 $
 

and this prevents dominant alternatives. However, I would like to use some extra knowledge that I have i.e., which attributes are most important. For simplicity let's assume the attributes are listed in increasing order of importance to respondents. Is it as simple as modifying the utility function to something like

Code: Select all

U(package1)=b2[0.02]*att2[12,18,24] + b3[0.03]*att3[30,55,80]+ b4[0.04]*att4[1,2,3] + b5[0.05]*att5[1,2,3] + b6[0.06]*att6[50,75,100] + b7[0.07]*att7[1,2,3] /
U(package2)=b2*att2+ b3*att3+ b4*att4+ b5*att5+ b6*att6+ b7*att7 $

I'm a bit concerned about the difference in magnitudes for the different attribute levels; is it generally desirable to have similar magnitudes across all the attributes? If so, which (if any) of the following is the better strategy
1) Should I re-scale the coefficients according to the level values e.g. ... b5[1]*att5[1,2,3] + b6[0.06]*att6[50,75,100]+...
2) Should I use coded attribute levels e.g... b2[0.02]*att2[0,1,2] + b3[0.03]*att3[0,1,2]+....

On a related note, if I use very small values [0.01] for my parameter estimates, my S (Sample size) number is huge [5,000] whereas if I use values on the order of [0.1] the size of S becomes much more realistic [50]. Is it a bad idea to assume priors of the order 0.1?

Thank you for any help you can provide & thanks for such a useful forum,

-Larmor

[Michiel Bliemer]

Since you are using the D-error as efficiency measure, scaling of the variables is not necessary. A D-optimal design will remain a D-optimal design even when you scale all the variables to have the same unit or range. Note that the A-error does not have this property. So it is fine to mix levels with range 10-80 with variables that range 1-3, and also priors that are 0.01 with priors that are 1.

Please do NOT just increase the priors (from 0.01 to 0.1) to improve the S-estimates, as that is merely tricking yourself. The priors should be as close as possible to the real value, and if the real value is 0.01, you cannot just change it to 0.1.

You can only influence the standard errors by changing the levels in your attributes. So instead of [1,2,3] you could use [1,3,5] IF this would make sense. The wider the range, the smaller the standard errors. However, the levels need to be realistic, so it is not always possible to do this. For the same reason will dummy variables always be harder to estimate, as the range is limited to [0,1].

Michiel